By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics signify probably the most vital contributions to our figuring out of the complicated stability among good and risky motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the life of targeted orbits and invariant measures of the process, which own a really wealthy dynamical and geometric constitution. particularly, the linked invariant units play a number one function in picking the worldwide dynamics of the procedure. This publication presents a accomplished creation to Mather’s thought, and will function an interdisciplinary bridge for researchers and scholars from varied fields looking to acquaint themselves with the topic.
Starting with the mathematical historical past from which Mather’s idea was once born, Alfonso Sorrentino first specializes in the middle questions the idea goals to answer—notably the future of damaged invariant KAM tori and the onset of chaos—and describes the way it may be considered as a average counterpart of KAM thought. He achieves this by means of guiding readers via an in depth illustrative instance, which additionally offers the root for introducing the most rules and ideas of the final concept. Sorrentino then describes the entire thought and its next advancements and purposes of their complete generality.
Shedding new gentle on John Mather’s innovative rules, this publication is sure to turn into a foundational textual content within the glossy examine of Hamiltonian systems.
Read Online or Download Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes) PDF
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Additional resources for Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes)
Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes) by Alfonso Sorrentino